Nuprl Lemma : assert_pushup_example
4 < 3 ∨ (3 ≤ 5)
Proof
Definitions occuring in Statement :
less_than: a < b,
le: A ≤ B,
or: P ∨ Q,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
lt_int: i <z j,
le_int: i ≤z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bor: p ∨bq,
assert: ↑b,
btrue: tt,
true: True
Lemmas referenced :
or_wf,
less_than_wf,
le_wf,
assert_wf,
lt_int_wf,
le_int_wf,
bor_wf,
iff_transitivity,
assert_of_lt_int,
assert_of_le_int,
iff_weakening_uiff,
assert_of_bor
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
sqequalRule,
imageElimination,
productElimination,
voidElimination,
independent_functionElimination,
independent_pairFormation,
lambdaFormation,
orFunctionality,
independent_isectElimination,
dependent_functionElimination
Latex:
4 < 3 \mvee{} (3 \mleq{} 5)
Date html generated:
2016_05_13-PM-04_03_28
Last ObjectModification:
2015_12_26-AM-10_56_00
Theory : int_1
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