Nuprl Lemma : lt_int_eq_true_elim
∀[i,j:ℤ]. i < j supposing i <z j = tt
Proof
Definitions occuring in Statement :
lt_int: i <z j,
btrue: tt,
bool: 𝔹,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
equal-wf-base,
bool_wf,
int_subtype_base,
member-less_than,
uiff_transitivity,
assert_wf,
lt_int_wf,
less_than_wf,
eqtt_to_assert,
assert_of_lt_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
isect_memberEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
intEquality,
independent_functionElimination,
productElimination
Latex:
\mforall{}[i,j:\mBbbZ{}]. i < j supposing i <z j = tt
Date html generated:
2019_06_20-AM-11_33_13
Last ObjectModification:
2018_09_26-PM-00_12_08
Theory : int_1
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