Nuprl Lemma : lifting-add-spread-2
∀[a:ℤ]. ∀[b,C:Top]. a + let x,y = b in C[x;y] ~ let x,y = b in a + C[x;y] supposing (a)↓
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
spread: spread def,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
has-value: (a)↓,
subtype_rel: A ⊆r B,
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
prop: ℙ,
top: Top,
false: False
Lemmas referenced :
int_subtype_base,
value-type-has-value,
int-value-type,
equal_wf,
top_wf,
pair-eta,
has-value_wf_base,
is-exception_wf,
int-add-exception,
exception-not-value
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueAdd,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
extract_by_obid,
productElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
lambdaFormation,
isectElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
callbyvalueSpread,
productEquality,
sqleReflexivity,
addExceptionCases,
axiomSqleEquality,
spreadExceptionCases,
because_Cache,
exceptionSqequal,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[b,C:Top]. a + let x,y = b in C[x;y] \msim{} let x,y = b in a + C[x;y] supposing (a)\mdownarrow{}
Date html generated:
2017_04_14-AM-07_21_13
Last ObjectModification:
2017_02_27-PM-02_54_53
Theory : computation
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