Nuprl Lemma : eq_atom1_self
∀[x:Atom1]. (x =a1 x ~ tt)
Proof
Definitions occuring in Statement :
eq_atom: eq_atom$n(x;y),
atom: Atom$n,
btrue: tt,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
eq_atom_wf1,
assert_of_eq_atom1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
hypothesisEquality,
productElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
atomnEquality
Latex:
\mforall{}[x:Atom1]. (x =a1 x \msim{} tt)
Date html generated:
2016_05_13-PM-03_21_15
Last ObjectModification:
2015_12_26-AM-09_12_02
Theory : atom_1
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