Nuprl Lemma : evalall-append-sqle
∀a,b:Top. (evalall(a @ b) ≤ eval u = evalall(a) in eval v = evalall(b) in evalall(u @ v))
Proof
Definitions occuring in Statement :
append: as @ bs,
evalall: evalall(t),
callbyvalue: callbyvalue,
top: Top,
all: ∀x:A. B[x],
sqle: s ≤ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
append: as @ bs,
list_ind: list_ind,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
top: Top,
evalall: evalall(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
nat_plus: ℕ+,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
strict4: strict4(F),
and: P ∧ Q,
has-value: (a)↓,
or: P ∨ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
cons: [a / b],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
it: ⋅,
nil: []
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
base_wf,
fun_exp0_lemma,
istype-void,
strictness-apply,
strictness-callbyvalue,
bottom-sqle,
subtract-1-ge-0,
fun_exp_unroll_1,
lifting-strict-callbyvalue,
has-value_wf_base,
istype-base,
is-exception_wf,
cbv_sqle,
int_subtype_base,
has-value-implies-dec-ispair-2,
istype-top,
list_ind_cons_lemma,
evalall-sqequal,
has-value-implies-dec-isaxiom-2,
list_ind_nil_lemma,
cbv_bottom_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
sqleRule,
thin,
sqequalRule,
fixpointLeast,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
axiomSqleEquality,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
Error :dependent_set_memberEquality_alt,
baseClosed,
independent_pairFormation,
callbyvalueCallbyvalue,
callbyvalueReduce,
baseApply,
closedConclusion,
callbyvalueExceptionCases,
Error :inrFormation_alt,
imageMemberEquality,
imageElimination,
exceptionSqequal,
Error :inlFormation_alt,
because_Cache,
applyEquality,
unionElimination,
sqleReflexivity,
divergentSqle,
sqleTransitivity
Latex:
\mforall{}a,b:Top. (evalall(a @ b) \mleq{} eval u = evalall(a) in eval v = evalall(b) in evalall(u @ v))
Date html generated:
2019_06_20-PM-00_39_36
Last ObjectModification:
2018_10_03-PM-01_54_25
Theory : list_0
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