Nuprl Lemma : lifting-apply-less
∀[n,m,a,b,c:Top]. (if (n) < (m) then a else b c ~ if (n) < (m) then a c else (b c))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
less: if (a) < (b) then c else d,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T
Lemmas referenced :
top_wf,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-less
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueApply,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
applyExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[n,m,a,b,c:Top]. (if (n) < (m) then a else b c \msim{} if (n) < (m) then a c else (b c))
Date html generated:
2016_05_13-PM-03_42_54
Last ObjectModification:
2016_01_14-PM-07_08_32
Theory : computation
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