Nuprl Lemma : zero-add-sq
∀[x,y:Top]. (x + y ~ (x + 0) + y)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
and: P ∧ Q,
uimplies: b supposing a,
top: Top,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
add-associates,
istype-void,
zero-add,
int-add-exception,
has-value_wf_base,
is-exception_wf,
value-type-has-value,
int-value-type,
sqle_wf_base,
squash_wf,
true_wf,
istype-base,
add-comm,
subtype_rel_self,
iff_weakening_equal,
zero-add-sqle,
exception-not-value,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueAdd,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
productElimination,
instantiate,
extract_by_obid,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
Error :isect_memberEquality_alt,
voidElimination,
addEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
sqleReflexivity,
addExceptionCases,
axiomSqleEquality,
exceptionSqequal,
natural_numberEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
Error :equalityIstype,
applyEquality,
Error :lambdaEquality_alt,
imageElimination,
Error :universeIsType,
imageMemberEquality,
universeEquality,
axiomSqEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[x,y:Top]. (x + y \msim{} (x + 0) + y)
Date html generated:
2019_06_20-AM-11_22_07
Last ObjectModification:
2019_01_21-PM-03_53_18
Theory : arithmetic
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