Nuprl Lemma : test-sq-lift3
∀[x:Top]. (if (x) < (0) then 1 else (1 + 1) + 1 ~ if (x) < (0) then 2 else 3)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
less: if (a) < (b) then c else d,
add: n + m,
natural_number: $n,
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,
int-value-type,
value-type-has-value,
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,
callbyvalueAdd,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
productElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
addExceptionCases,
exceptionSqequal,
inrFormation,
intEquality,
imageMemberEquality,
imageElimination,
inlFormation,
sqequalAxiom
Latex:
\mforall{}[x:Top]. (if (x) < (0) then 1 else (1 + 1) + 1 \msim{} if (x) < (0) then 2 else 3)
Date html generated:
2016_05_15-PM-10_36_17
Last ObjectModification:
2016_01_16-PM-09_37_30
Theory : rationals
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